Topological properties and optimal routing algorithms for three dimensional hexagonal networks

2000 ◽  
Author(s):  
J. Carle ◽  
J.F. Myoupo
Keyword(s):  
Three Dimensional ◽  
Routing Algorithms ◽  
Optimal Routing ◽  
Topological Properties

scholarly journals Effect of the anisotropy of the cells on the topological properties of two- and three-dimensional froths

2001 ◽  
Vol 63 (6) ◽  
Author(s):  
Patrick Richard ◽  
Jean-Paul Troadec ◽  
Luc Oger ◽  
Annie Gervois
Keyword(s):  
Three Dimensional ◽  
Topological Properties

An Integrated Approach to Optimal Three Dimensional Layout and Routing

1998 ◽  
Vol 120 (3) ◽  
pp. 510-512 ◽  
Author(s):  
S. Szykman ◽  
J. Cagan ◽  
P. Weisser
Keyword(s):  
Simulated Annealing ◽  
Three Dimensional ◽  
Integrated Approach ◽  
Substantial Improvement ◽  
Routing Algorithms ◽  
Future Research ◽  
Test Case ◽  
Integrated Method ◽  
Route Design ◽  
Product Layout

This paper integrates simulated annealing-based component packing, layout and routing algorithms into a concurrent approach to product layout optimization. The design of a heat pump is presented to compare the integrated method to the previous sequential layout-then-route approach; results show a substantial improvement in route design with more organized component placements. The example is given in detail to provide a test case for future research in this area.

Body in Categories 6

2018 ◽  
Author(s):  
Christian Pfeiffer
Keyword(s):  
Three Dimensional ◽  
Basic Theory ◽  
Topological Properties ◽  
In Virtue Of

This chapter expands on the basic theory, which is presented in the Categories. It offers a treatment of the mereotopological properties of bodies, for instance, what belongs to them insofar as they are bodies of physical substances. Bodies are complete and perfect in virtue of being three‐dimensional. Body is prior to surfaces and lines and, because bodies are complete, there cannot be a four‐dimensional magnitude. The explanation offered is that certain topological properties are linked to and determined by the nature of the object in question. Body is a composite of the boundary and the interior or extension. A formal characterization of boundaries as limit entities is offered and it is argued that boundaries are dependent particulars. Similarly, the extension is ontologically dependent on bodies. Aristotle’s argument that the extension of objects is divisible into ever‐divisibles is revisited.

scholarly journals Optical framed knots as information carriers

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Hugo Larocque ◽  
Alessio D’Errico ◽  
Manuel F. Ferrer-Garcia ◽  
Avishy Carmi ◽  
Eliahu Cohen ◽  
...  
Keyword(s):  
Structured Light ◽  
Three Dimensional ◽  
Structural Features ◽  
Topological Invariants ◽  
Topological Properties ◽  
Optical Fields ◽  
Prime Factorization ◽  
Experimental Realization ◽  
Physical Systems ◽  
Modern Technologies

Abstract Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots. However, unlike simpler types of structured light, the topological properties of these optical fields have hitherto remained more of a fundamental curiosity as opposed to a feature that can be applied in modern technologies. Due to their robustness against external perturbations, topological invariants in physical systems are increasingly being considered as a means to encode information. Hence, structured light with topological properties could potentially be used for such purposes. Here, we introduce the experimental realization of structures known as framed knots within optical polarization fields. We further develop a protocol in which the topological properties of framed knots are used in conjunction with prime factorization to encode information.

Synthesis of Optimal Non-Orthogonal Routes

1995 ◽  
Author(s):  
Simon Szykman ◽  
Jonathan Cagan
Keyword(s):  
Simulated Annealing ◽  
Optimization Algorithm ◽  
Three Dimensional ◽  
Routing Algorithms ◽  
Engineering Applications ◽  
Routing Optimization ◽  
Novel Approach

Abstract This paper introduces a novel approach to three dimensional routing optimization. Examples of routing tasks for engineering applications include routing of pipes, wires and air ducts. Traditionally, routing algorithms perform Manhattan, or orthogonal, routing. Non-orthogonal routing can be less costly than Manhattan routing and for applications such as automotive or aerospace design, Manhattan routing is impractical due to spatial limitations. The research presented in this paper uses simulated annealing as the basis of a non-orthogonal routing optimization algorithm that avoids the drawbacks associated with Manhattan routing. Several examples comparing the two approaches are given.

Synthesis of Optimal Nonorthogonal Routes

1996 ◽  
Vol 118 (3) ◽  
pp. 419-424 ◽  
Author(s):  
S. Szykman ◽  
J. Cagan
Keyword(s):  
Simulated Annealing ◽  
Optimization Algorithm ◽  
Three Dimensional ◽  
Routing Algorithms ◽  
Engineering Applications ◽  
Routing Optimization ◽  
Novel Approach

This paper introduces a novel approach to three dimensional routing optimization. Examples of routing tasks for engineering applications include routing of pipes, wires and air ducts. Traditionally, routing algorithms perform Manhattan, or orthogonal, routing. Nonorthogonal routing can be less costly than Manhattan routing and for applications such as automotive or aerospace design, Manhattan routing is impractical due to spatial limitations. The research presented in this paper uses simulated annealing as the basis of a nonorthogonal routing optimization algorithm. Several examples comparing the two approaches are given.

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